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Mathematics
Mathematics
Problem
If
I
n
=
∫
0
π
4
tan
n
x
d
x
I_n = \int_{0}^{\frac{\pi}{4}} \tan^n x dx
I
n
=
∫
0
4
π
tan
n
x
d
x
, then show that
n
(
I
n
−
1
+
I
n
+
1
)
=
1
n(I_{n-1} + I_{n+1}) = 1
n
(
I
n
−
1
+
I
n
+
1
)
=
1
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